A global min is a point where the y-value is the least of all possible y-values in the range of the function. No other output will be less.
I know how to solve for local min and max.
For instance,
F = 2x^2 + y^2 +4x -4y +5
The point (-1,2) is a local minimum, but my book also points out that it is a global minimum.
Can anyone tell me how to find the global max/min after I have found critical points and local max/min.
If you have found all the local minima, then (assuming the function doesn't go off to at any point), the global minimum is the smallest of the local minima.
So what you need to do, to prove a global minimum, is show that it's the smallest of the local minima, and that the curve does not go off to .
Yes I know you weren't told to prove that it is a global minimum, consider this post a "for information" one.